Related papers: Approximation of some classes of set-valued period…

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…

We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…

Various versions of the classical definitions of (one- and twosided) almost periodicity for functions on groups with values in a uniform space are formulated and their equivalence is shown.

For a function $f$ that is piecewise analytic on a quasi-smooth arc $\mathcal{L}$ and any $0<\sigma<1$ we construct a sequence of "near-best" polynomials that converge at a rate $e^{-n^{\sigma}}$ at each point of analyticity of $f$ and are…

We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…

Let a $2\pi$-periodic function $f\in\Bbb C$ changes its monotonicity at a finitely even number of points $y_i$ of the period. The degree of approximation of this $f$ by trigonometric polynomials which are comonotone with it, i.e. that…

In this survey, we use (more or less) elementary means to establish the well-known result that for any given smooth multivariate function, the respective multivariate Bernstein polynomials converge to that function in all derivatives on…

We define generalized bivariate polynomials, from which upon specification of initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in…

It is a natural question to ask which plurisubharmonic functions admit a 'nice' approximation in the sense of a decreasing equisingular approximation with analytic singularities. For arbitrary toric plurisubharmonic functions, we give a…

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…

Four families of generalizations of trigonometric functions were recently introduced. In the paper the functions are transformed into four families of orthogonal polynomials depending on two variables. Recurrence relations for construction…

A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…

The main goal in this manuscript is to present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…

We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies. We prove that polystar bodies are uniformly dense in…